The entropy of holomorphic correspondences: exact computations and rational semigroups
Dynamical Systems
2021-05-18 v2 Complex Variables
Abstract
We study two notions of topological entropy of correspondences introduced by Friedland and Dinh-Sibony. Upper bounds are known for both. We identify a class of holomorphic correspondences whose entropy in the sense of Dinh-Sibony equals the known upper bound. This provides an exact computation of the entropy for rational semigroups. We also explore a connection between these two notions of entropy.
Keywords
Cite
@article{arxiv.2004.13691,
title = {The entropy of holomorphic correspondences: exact computations and rational semigroups},
author = {Gautam Bharali and Shrihari Sridharan},
journal= {arXiv preprint arXiv:2004.13691},
year = {2021}
}
Comments
18 pages; added references; added a new expository section (Subsection 1.1) and further exposition in Section 5; to appear in Ann. Acad. Sci. Fennicae